| Project/Area Number |
15340052
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
YANAGIDA Eiji Tohoku University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (80174548)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAGI Izumi Tohoku University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (40154744)
CHIHARA Hiroyuki Tohoku University, Graduate School of Science, Associate Professor, 大学院理学研究科, 助教授 (70273068)
EI Shin-Ichiro Kyushu University, Graduate School of Science, Professor, 大学院数理学研究院, 教授 (30201362)
MIZOGUCHI Noriko Tohoku University, Faculty of Education, Associate Professor, 教育学部, 教授 (00251570)
NINOMIYA Hirokazu Ryukoku University, Faculty of Sciencde and Enginnering, Associate Professor, 理工学部, 助教授 (90251610)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥16,100,000 (Direct Cost: ¥16,100,000)
Fiscal Year 2006: ¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2005: ¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 2004: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2003: ¥3,900,000 (Direct Cost: ¥3,900,000)
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| Keywords | nonlinearity / diffusion / singularity / dynamics / reaction-diffusion systems / partial differential equations / pattern formation / analysis / 爆発 / 凝集 / パターン |
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| Research Abstract |
For the understanding of various nonlinear phenomena observed in nonlinear diffusive systems, a key is to analyze the mechanism for the appearance of singularities such as blow-up, concentration, and transition layers. In this research, we aim to develop new methods for the analysis of stable pattern formation, pattern dynamics in higher dimensional space, and long-time behavior of scalar reaction-diffusion equations.
First, we studied the stability of stationary solutions in shadow systems, and showed that the convexity of spatial structure plays an important role under the assumption that nonlinear term has skew-gradient structure.
Second, we studied the behavior of solutions of Fujita-type equations, and made clear the relation between the convergence rate of solutions and decay rate of initial data.
Third, we studied a minimization problem for the principal eigenvalue of elliptic problem with indefinite weight. We showed the minimizer must be of bang-bang type, and obtained a minimizer in the case of one-dimensional space. We also considered the case of cylindrical domain, and found that a sort of symmetry-breaking must occur.
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